R Under development (unstable) (2023-08-20 r84995 ucrt) -- "Unsuffered Consequences"
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> # Also see the first test in rotations.R
> # compares varimax to Varimax to 0.001 discrepancy
> 
>  Sys.getenv("R_LIBS")
[1] "D:\\temp\\RtmpAj55YZ\\RLIBS_2d3e42b45675f"
>  library()
>  require("GPArotation")
Loading required package: GPArotation
>  search()
 [1] ".GlobalEnv"          "package:GPArotation" "package:stats"      
 [4] "package:graphics"    "package:grDevices"   "package:utils"      
 [7] "package:datasets"    "package:methods"     "Autoloads"          
[10] "package:base"       
>  Sys.info()
       sysname        release        version       nodename        machine 
     "Windows"   "Server x64"  "build 20348"     "CRANWIN3"       "x86-64" 
         login           user effective_user 
        "CRAN"         "CRAN"         "CRAN" 
> 
> ### note that this is a slightly lower bar than other tests
> ### to correct for the built-in varimax function working differently
> ### than GPA, and to ensure Varimax convergence
> ### these are differences in the 4th decimal or better
>  fuzz <- 1e-4
> ###
>  all.ok <- TRUE  
> 
> sortFac <- function(x){  # Based on Fungible faSort 
+   vx <- order(colSums(x$loadings^2), decreasing = TRUE)
+   Dsgn <- diag(sign(colSums(x$loadings^3))) [ , vx]
+   x$Th <- x$Th %*% Dsgn 
+   x$loadings <- x$loadings %*% Dsgn
+   if ("Phi" %in% names(x)) { 
+     x$Phi <- diag(1/diag(Dsgn)) %*% x$Phi %*% Dsgn
+     }
+   x 
+ } 
> data(Thurstone, package="GPArotation")
> yv1 <- varimax(box20, normalize = FALSE, eps = 1e-7) #built-in R
> names(yv1) <- c("loadings","Th")
> yv1 <- sortFac(yv1)
> yv2 <- sortFac(Varimax(box20, normalize = FALSE, maxit = 10000, eps = 1e-7)) #GPArotation version
> # yv.diff <- unclass(yv1$loadings) - unclass(yv2$loadings)
> # max(abs(yv.diff))
> 
> 
>  if( fuzz < max(abs(yv1$loadings - yv2$loadings))) {
+     cat("Calculated varimax is not the same as Varimax:\n")
+     # print(yv2$loadings, digits=18)
+     cat("difference:\n")
+     print(yv1$loadings - yv2$loadings, digits=18)
+     all.ok <- FALSE  
+     } 
> 
> 
> proc.time()
   user  system elapsed 
   0.26    0.04    0.34